Properties

Label 4033.2.a.d.1.1
Level 4033
Weight 2
Character 4033.1
Self dual Yes
Analytic conductor 32.204
Analytic rank 1
Dimension 79
CM No

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Newspace parameters

Level: \( N \) = \( 4033 = 37 \cdot 109 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4033.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.2036671352\)
Analytic rank: \(1\)
Dimension: \(79\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 4033.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.81086 q^{2}\) \(-2.68213 q^{3}\) \(+5.90091 q^{4}\) \(+2.99603 q^{5}\) \(+7.53909 q^{6}\) \(+4.86255 q^{7}\) \(-10.9649 q^{8}\) \(+4.19384 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.81086 q^{2}\) \(-2.68213 q^{3}\) \(+5.90091 q^{4}\) \(+2.99603 q^{5}\) \(+7.53909 q^{6}\) \(+4.86255 q^{7}\) \(-10.9649 q^{8}\) \(+4.19384 q^{9}\) \(-8.42140 q^{10}\) \(-1.33120 q^{11}\) \(-15.8270 q^{12}\) \(-3.27896 q^{13}\) \(-13.6679 q^{14}\) \(-8.03574 q^{15}\) \(+19.0189 q^{16}\) \(-4.03462 q^{17}\) \(-11.7883 q^{18}\) \(+4.45868 q^{19}\) \(+17.6793 q^{20}\) \(-13.0420 q^{21}\) \(+3.74181 q^{22}\) \(-1.35388 q^{23}\) \(+29.4093 q^{24}\) \(+3.97617 q^{25}\) \(+9.21669 q^{26}\) \(-3.20203 q^{27}\) \(+28.6935 q^{28}\) \(+5.93104 q^{29}\) \(+22.5873 q^{30}\) \(-2.35996 q^{31}\) \(-31.5296 q^{32}\) \(+3.57045 q^{33}\) \(+11.3407 q^{34}\) \(+14.5683 q^{35}\) \(+24.7475 q^{36}\) \(-1.00000 q^{37}\) \(-12.5327 q^{38}\) \(+8.79462 q^{39}\) \(-32.8511 q^{40}\) \(-7.42395 q^{41}\) \(+36.6592 q^{42}\) \(-4.67678 q^{43}\) \(-7.85528 q^{44}\) \(+12.5649 q^{45}\) \(+3.80557 q^{46}\) \(-7.56953 q^{47}\) \(-51.0113 q^{48}\) \(+16.6444 q^{49}\) \(-11.1764 q^{50}\) \(+10.8214 q^{51}\) \(-19.3489 q^{52}\) \(+2.65719 q^{53}\) \(+9.00046 q^{54}\) \(-3.98830 q^{55}\) \(-53.3174 q^{56}\) \(-11.9588 q^{57}\) \(-16.6713 q^{58}\) \(-5.14063 q^{59}\) \(-47.4182 q^{60}\) \(-13.5372 q^{61}\) \(+6.63350 q^{62}\) \(+20.3928 q^{63}\) \(+50.5875 q^{64}\) \(-9.82386 q^{65}\) \(-10.0360 q^{66}\) \(-14.4823 q^{67}\) \(-23.8079 q^{68}\) \(+3.63129 q^{69}\) \(-40.9495 q^{70}\) \(-11.0342 q^{71}\) \(-45.9850 q^{72}\) \(+7.04248 q^{73}\) \(+2.81086 q^{74}\) \(-10.6646 q^{75}\) \(+26.3103 q^{76}\) \(-6.47302 q^{77}\) \(-24.7204 q^{78}\) \(+14.1106 q^{79}\) \(+56.9812 q^{80}\) \(-3.99323 q^{81}\) \(+20.8676 q^{82}\) \(+2.53040 q^{83}\) \(-76.9597 q^{84}\) \(-12.0878 q^{85}\) \(+13.1458 q^{86}\) \(-15.9078 q^{87}\) \(+14.5965 q^{88}\) \(+1.25085 q^{89}\) \(-35.3180 q^{90}\) \(-15.9441 q^{91}\) \(-7.98914 q^{92}\) \(+6.32972 q^{93}\) \(+21.2768 q^{94}\) \(+13.3583 q^{95}\) \(+84.5667 q^{96}\) \(-11.3637 q^{97}\) \(-46.7850 q^{98}\) \(-5.58283 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut -\mathstrut 13q^{10} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut -\mathstrut 40q^{12} \) \(\mathstrut -\mathstrut 18q^{13} \) \(\mathstrut -\mathstrut 42q^{14} \) \(\mathstrut -\mathstrut 49q^{15} \) \(\mathstrut +\mathstrut 83q^{16} \) \(\mathstrut -\mathstrut 62q^{17} \) \(\mathstrut -\mathstrut 33q^{18} \) \(\mathstrut -\mathstrut 25q^{19} \) \(\mathstrut -\mathstrut 39q^{20} \) \(\mathstrut -\mathstrut 15q^{21} \) \(\mathstrut -\mathstrut 31q^{22} \) \(\mathstrut -\mathstrut 94q^{23} \) \(\mathstrut -\mathstrut 39q^{24} \) \(\mathstrut +\mathstrut 71q^{25} \) \(\mathstrut -\mathstrut 35q^{26} \) \(\mathstrut -\mathstrut 47q^{27} \) \(\mathstrut -\mathstrut 13q^{28} \) \(\mathstrut -\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 15q^{30} \) \(\mathstrut -\mathstrut 37q^{31} \) \(\mathstrut -\mathstrut 105q^{32} \) \(\mathstrut -\mathstrut 60q^{33} \) \(\mathstrut +\mathstrut 9q^{34} \) \(\mathstrut -\mathstrut 60q^{35} \) \(\mathstrut +\mathstrut 43q^{36} \) \(\mathstrut -\mathstrut 79q^{37} \) \(\mathstrut -\mathstrut 80q^{38} \) \(\mathstrut -\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 64q^{40} \) \(\mathstrut -\mathstrut 37q^{41} \) \(\mathstrut -\mathstrut 30q^{42} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut -\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 8q^{45} \) \(\mathstrut +\mathstrut 61q^{46} \) \(\mathstrut -\mathstrut 148q^{47} \) \(\mathstrut -\mathstrut 39q^{48} \) \(\mathstrut +\mathstrut 82q^{49} \) \(\mathstrut -\mathstrut 90q^{50} \) \(\mathstrut -\mathstrut 45q^{51} \) \(\mathstrut -\mathstrut 27q^{52} \) \(\mathstrut -\mathstrut 70q^{53} \) \(\mathstrut -\mathstrut 41q^{54} \) \(\mathstrut -\mathstrut 105q^{55} \) \(\mathstrut -\mathstrut 68q^{56} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut -\mathstrut 14q^{58} \) \(\mathstrut -\mathstrut 96q^{59} \) \(\mathstrut -\mathstrut 74q^{60} \) \(\mathstrut -\mathstrut 21q^{61} \) \(\mathstrut +\mathstrut 4q^{62} \) \(\mathstrut -\mathstrut 60q^{63} \) \(\mathstrut +\mathstrut 132q^{64} \) \(\mathstrut -\mathstrut 15q^{65} \) \(\mathstrut +\mathstrut 71q^{66} \) \(\mathstrut -\mathstrut 44q^{67} \) \(\mathstrut -\mathstrut 166q^{68} \) \(\mathstrut -\mathstrut 72q^{69} \) \(\mathstrut -\mathstrut 9q^{70} \) \(\mathstrut -\mathstrut 55q^{71} \) \(\mathstrut -\mathstrut 126q^{72} \) \(\mathstrut -\mathstrut 27q^{73} \) \(\mathstrut +\mathstrut 11q^{74} \) \(\mathstrut -\mathstrut 39q^{75} \) \(\mathstrut -\mathstrut 4q^{76} \) \(\mathstrut -\mathstrut 104q^{77} \) \(\mathstrut -\mathstrut 47q^{78} \) \(\mathstrut -\mathstrut 49q^{79} \) \(\mathstrut -\mathstrut 82q^{80} \) \(\mathstrut +\mathstrut 55q^{81} \) \(\mathstrut +\mathstrut 20q^{82} \) \(\mathstrut -\mathstrut 52q^{83} \) \(\mathstrut -\mathstrut 29q^{84} \) \(\mathstrut +\mathstrut 3q^{85} \) \(\mathstrut -\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 113q^{87} \) \(\mathstrut +\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 68q^{89} \) \(\mathstrut -\mathstrut 39q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 179q^{92} \) \(\mathstrut -\mathstrut 53q^{93} \) \(\mathstrut -\mathstrut 33q^{94} \) \(\mathstrut -\mathstrut 86q^{95} \) \(\mathstrut +\mathstrut 33q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut -\mathstrut 116q^{98} \) \(\mathstrut +\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.81086 −1.98758 −0.993788 0.111293i \(-0.964501\pi\)
−0.993788 + 0.111293i \(0.964501\pi\)
\(3\) −2.68213 −1.54853 −0.774265 0.632861i \(-0.781880\pi\)
−0.774265 + 0.632861i \(0.781880\pi\)
\(4\) 5.90091 2.95046
\(5\) 2.99603 1.33986 0.669932 0.742423i \(-0.266323\pi\)
0.669932 + 0.742423i \(0.266323\pi\)
\(6\) 7.53909 3.07782
\(7\) 4.86255 1.83787 0.918936 0.394407i \(-0.129050\pi\)
0.918936 + 0.394407i \(0.129050\pi\)
\(8\) −10.9649 −3.87668
\(9\) 4.19384 1.39795
\(10\) −8.42140 −2.66308
\(11\) −1.33120 −0.401371 −0.200686 0.979656i \(-0.564317\pi\)
−0.200686 + 0.979656i \(0.564317\pi\)
\(12\) −15.8270 −4.56887
\(13\) −3.27896 −0.909421 −0.454710 0.890639i \(-0.650257\pi\)
−0.454710 + 0.890639i \(0.650257\pi\)
\(14\) −13.6679 −3.65291
\(15\) −8.03574 −2.07482
\(16\) 19.0189 4.75473
\(17\) −4.03462 −0.978539 −0.489270 0.872133i \(-0.662737\pi\)
−0.489270 + 0.872133i \(0.662737\pi\)
\(18\) −11.7883 −2.77852
\(19\) 4.45868 1.02289 0.511446 0.859315i \(-0.329110\pi\)
0.511446 + 0.859315i \(0.329110\pi\)
\(20\) 17.6793 3.95321
\(21\) −13.0420 −2.84600
\(22\) 3.74181 0.797756
\(23\) −1.35388 −0.282304 −0.141152 0.989988i \(-0.545081\pi\)
−0.141152 + 0.989988i \(0.545081\pi\)
\(24\) 29.4093 6.00315
\(25\) 3.97617 0.795235
\(26\) 9.21669 1.80754
\(27\) −3.20203 −0.616232
\(28\) 28.6935 5.42256
\(29\) 5.93104 1.10137 0.550683 0.834714i \(-0.314367\pi\)
0.550683 + 0.834714i \(0.314367\pi\)
\(30\) 22.5873 4.12386
\(31\) −2.35996 −0.423861 −0.211930 0.977285i \(-0.567975\pi\)
−0.211930 + 0.977285i \(0.567975\pi\)
\(32\) −31.5296 −5.57371
\(33\) 3.57045 0.621536
\(34\) 11.3407 1.94492
\(35\) 14.5683 2.46250
\(36\) 24.7475 4.12458
\(37\) −1.00000 −0.164399
\(38\) −12.5327 −2.03308
\(39\) 8.79462 1.40827
\(40\) −32.8511 −5.19422
\(41\) −7.42395 −1.15943 −0.579713 0.814821i \(-0.696835\pi\)
−0.579713 + 0.814821i \(0.696835\pi\)
\(42\) 36.6592 5.65664
\(43\) −4.67678 −0.713203 −0.356601 0.934257i \(-0.616065\pi\)
−0.356601 + 0.934257i \(0.616065\pi\)
\(44\) −7.85528 −1.18423
\(45\) 12.5649 1.87306
\(46\) 3.80557 0.561101
\(47\) −7.56953 −1.10413 −0.552064 0.833801i \(-0.686160\pi\)
−0.552064 + 0.833801i \(0.686160\pi\)
\(48\) −51.0113 −7.36284
\(49\) 16.6444 2.37777
\(50\) −11.1764 −1.58059
\(51\) 10.8214 1.51530
\(52\) −19.3489 −2.68321
\(53\) 2.65719 0.364994 0.182497 0.983206i \(-0.441582\pi\)
0.182497 + 0.983206i \(0.441582\pi\)
\(54\) 9.00046 1.22481
\(55\) −3.98830 −0.537783
\(56\) −53.3174 −7.12483
\(57\) −11.9588 −1.58398
\(58\) −16.6713 −2.18905
\(59\) −5.14063 −0.669254 −0.334627 0.942351i \(-0.608610\pi\)
−0.334627 + 0.942351i \(0.608610\pi\)
\(60\) −47.4182 −6.12166
\(61\) −13.5372 −1.73326 −0.866628 0.498954i \(-0.833718\pi\)
−0.866628 + 0.498954i \(0.833718\pi\)
\(62\) 6.63350 0.842455
\(63\) 20.3928 2.56925
\(64\) 50.5875 6.32343
\(65\) −9.82386 −1.21850
\(66\) −10.0360 −1.23535
\(67\) −14.4823 −1.76930 −0.884650 0.466256i \(-0.845603\pi\)
−0.884650 + 0.466256i \(0.845603\pi\)
\(68\) −23.8079 −2.88714
\(69\) 3.63129 0.437156
\(70\) −40.9495 −4.89440
\(71\) −11.0342 −1.30952 −0.654758 0.755839i \(-0.727229\pi\)
−0.654758 + 0.755839i \(0.727229\pi\)
\(72\) −45.9850 −5.41938
\(73\) 7.04248 0.824260 0.412130 0.911125i \(-0.364785\pi\)
0.412130 + 0.911125i \(0.364785\pi\)
\(74\) 2.81086 0.326755
\(75\) −10.6646 −1.23144
\(76\) 26.3103 3.01800
\(77\) −6.47302 −0.737669
\(78\) −24.7204 −2.79903
\(79\) 14.1106 1.58757 0.793783 0.608201i \(-0.208108\pi\)
0.793783 + 0.608201i \(0.208108\pi\)
\(80\) 56.9812 6.37069
\(81\) −3.99323 −0.443693
\(82\) 20.8676 2.30445
\(83\) 2.53040 0.277748 0.138874 0.990310i \(-0.455652\pi\)
0.138874 + 0.990310i \(0.455652\pi\)
\(84\) −76.9597 −8.39700
\(85\) −12.0878 −1.31111
\(86\) 13.1458 1.41754
\(87\) −15.9078 −1.70550
\(88\) 14.5965 1.55599
\(89\) 1.25085 0.132590 0.0662948 0.997800i \(-0.478882\pi\)
0.0662948 + 0.997800i \(0.478882\pi\)
\(90\) −35.3180 −3.72284
\(91\) −15.9441 −1.67140
\(92\) −7.98914 −0.832926
\(93\) 6.32972 0.656361
\(94\) 21.2768 2.19454
\(95\) 13.3583 1.37054
\(96\) 84.5667 8.63105
\(97\) −11.3637 −1.15381 −0.576906 0.816811i \(-0.695740\pi\)
−0.576906 + 0.816811i \(0.695740\pi\)
\(98\) −46.7850 −4.72600
\(99\) −5.58283 −0.561096
\(100\) 23.4630 2.34630
\(101\) −3.23748 −0.322141 −0.161071 0.986943i \(-0.551495\pi\)
−0.161071 + 0.986943i \(0.551495\pi\)
\(102\) −30.4174 −3.01177
\(103\) 6.92612 0.682451 0.341226 0.939981i \(-0.389158\pi\)
0.341226 + 0.939981i \(0.389158\pi\)
\(104\) 35.9535 3.52553
\(105\) −39.0742 −3.81325
\(106\) −7.46899 −0.725453
\(107\) 2.27249 0.219690 0.109845 0.993949i \(-0.464965\pi\)
0.109845 + 0.993949i \(0.464965\pi\)
\(108\) −18.8949 −1.81816
\(109\) −1.00000 −0.0957826
\(110\) 11.2105 1.06888
\(111\) 2.68213 0.254577
\(112\) 92.4805 8.73858
\(113\) −14.0491 −1.32163 −0.660814 0.750550i \(-0.729789\pi\)
−0.660814 + 0.750550i \(0.729789\pi\)
\(114\) 33.6144 3.14828
\(115\) −4.05627 −0.378249
\(116\) 34.9985 3.24953
\(117\) −13.7514 −1.27132
\(118\) 14.4496 1.33019
\(119\) −19.6186 −1.79843
\(120\) 88.1111 8.04340
\(121\) −9.22791 −0.838901
\(122\) 38.0510 3.44498
\(123\) 19.9120 1.79541
\(124\) −13.9259 −1.25058
\(125\) −3.06741 −0.274358
\(126\) −57.3211 −5.10657
\(127\) −15.4797 −1.37360 −0.686799 0.726847i \(-0.740985\pi\)
−0.686799 + 0.726847i \(0.740985\pi\)
\(128\) −79.1347 −6.99459
\(129\) 12.5438 1.10442
\(130\) 27.6135 2.42186
\(131\) −20.7811 −1.81565 −0.907825 0.419350i \(-0.862258\pi\)
−0.907825 + 0.419350i \(0.862258\pi\)
\(132\) 21.0689 1.83381
\(133\) 21.6806 1.87994
\(134\) 40.7078 3.51662
\(135\) −9.59338 −0.825667
\(136\) 44.2392 3.79348
\(137\) 13.5445 1.15719 0.578593 0.815616i \(-0.303602\pi\)
0.578593 + 0.815616i \(0.303602\pi\)
\(138\) −10.2070 −0.868881
\(139\) −9.82763 −0.833568 −0.416784 0.909005i \(-0.636843\pi\)
−0.416784 + 0.909005i \(0.636843\pi\)
\(140\) 85.9664 7.26549
\(141\) 20.3025 1.70978
\(142\) 31.0155 2.60276
\(143\) 4.36495 0.365015
\(144\) 79.7623 6.64686
\(145\) 17.7696 1.47568
\(146\) −19.7954 −1.63828
\(147\) −44.6425 −3.68205
\(148\) −5.90091 −0.485052
\(149\) 16.7138 1.36925 0.684624 0.728896i \(-0.259966\pi\)
0.684624 + 0.728896i \(0.259966\pi\)
\(150\) 29.9767 2.44759
\(151\) −8.08426 −0.657888 −0.328944 0.944349i \(-0.606693\pi\)
−0.328944 + 0.944349i \(0.606693\pi\)
\(152\) −48.8890 −3.96542
\(153\) −16.9205 −1.36795
\(154\) 18.1947 1.46617
\(155\) −7.07049 −0.567916
\(156\) 51.8962 4.15502
\(157\) 5.16429 0.412155 0.206078 0.978536i \(-0.433930\pi\)
0.206078 + 0.978536i \(0.433930\pi\)
\(158\) −39.6629 −3.15541
\(159\) −7.12695 −0.565204
\(160\) −94.4637 −7.46801
\(161\) −6.58333 −0.518839
\(162\) 11.2244 0.881872
\(163\) 9.19682 0.720351 0.360175 0.932885i \(-0.382717\pi\)
0.360175 + 0.932885i \(0.382717\pi\)
\(164\) −43.8080 −3.42083
\(165\) 10.6972 0.832773
\(166\) −7.11259 −0.552044
\(167\) 0.805841 0.0623579 0.0311789 0.999514i \(-0.490074\pi\)
0.0311789 + 0.999514i \(0.490074\pi\)
\(168\) 143.004 11.0330
\(169\) −2.24840 −0.172954
\(170\) 33.9771 2.60593
\(171\) 18.6990 1.42995
\(172\) −27.5973 −2.10427
\(173\) −20.6448 −1.56959 −0.784797 0.619753i \(-0.787233\pi\)
−0.784797 + 0.619753i \(0.787233\pi\)
\(174\) 44.7147 3.38981
\(175\) 19.3343 1.46154
\(176\) −25.3180 −1.90841
\(177\) 13.7879 1.03636
\(178\) −3.51595 −0.263532
\(179\) 6.21114 0.464243 0.232121 0.972687i \(-0.425433\pi\)
0.232121 + 0.972687i \(0.425433\pi\)
\(180\) 74.1441 5.52637
\(181\) −3.17195 −0.235769 −0.117885 0.993027i \(-0.537611\pi\)
−0.117885 + 0.993027i \(0.537611\pi\)
\(182\) 44.8166 3.32203
\(183\) 36.3085 2.68400
\(184\) 14.8452 1.09440
\(185\) −2.99603 −0.220272
\(186\) −17.7919 −1.30457
\(187\) 5.37088 0.392758
\(188\) −44.6671 −3.25768
\(189\) −15.5701 −1.13256
\(190\) −37.5484 −2.72404
\(191\) −25.3004 −1.83068 −0.915338 0.402686i \(-0.868077\pi\)
−0.915338 + 0.402686i \(0.868077\pi\)
\(192\) −135.682 −9.79203
\(193\) −8.60196 −0.619182 −0.309591 0.950870i \(-0.600192\pi\)
−0.309591 + 0.950870i \(0.600192\pi\)
\(194\) 31.9418 2.29329
\(195\) 26.3489 1.88688
\(196\) 98.2172 7.01551
\(197\) 4.89769 0.348946 0.174473 0.984662i \(-0.444178\pi\)
0.174473 + 0.984662i \(0.444178\pi\)
\(198\) 15.6925 1.11522
\(199\) −2.21511 −0.157025 −0.0785126 0.996913i \(-0.525017\pi\)
−0.0785126 + 0.996913i \(0.525017\pi\)
\(200\) −43.5983 −3.08287
\(201\) 38.8436 2.73981
\(202\) 9.10009 0.640280
\(203\) 28.8400 2.02417
\(204\) 63.8560 4.47082
\(205\) −22.2423 −1.55347
\(206\) −19.4683 −1.35642
\(207\) −5.67797 −0.394646
\(208\) −62.3623 −4.32405
\(209\) −5.93539 −0.410560
\(210\) 109.832 7.57913
\(211\) 17.7341 1.22087 0.610433 0.792068i \(-0.290995\pi\)
0.610433 + 0.792068i \(0.290995\pi\)
\(212\) 15.6799 1.07690
\(213\) 29.5951 2.02782
\(214\) −6.38765 −0.436651
\(215\) −14.0118 −0.955594
\(216\) 35.1100 2.38893
\(217\) −11.4754 −0.779002
\(218\) 2.81086 0.190375
\(219\) −18.8889 −1.27639
\(220\) −23.5346 −1.58670
\(221\) 13.2294 0.889904
\(222\) −7.53909 −0.505991
\(223\) −17.4275 −1.16703 −0.583517 0.812101i \(-0.698324\pi\)
−0.583517 + 0.812101i \(0.698324\pi\)
\(224\) −153.315 −10.2438
\(225\) 16.6754 1.11170
\(226\) 39.4900 2.62683
\(227\) −4.26191 −0.282873 −0.141436 0.989947i \(-0.545172\pi\)
−0.141436 + 0.989947i \(0.545172\pi\)
\(228\) −70.5677 −4.67346
\(229\) 18.5238 1.22409 0.612045 0.790823i \(-0.290347\pi\)
0.612045 + 0.790823i \(0.290347\pi\)
\(230\) 11.4016 0.751798
\(231\) 17.3615 1.14230
\(232\) −65.0333 −4.26964
\(233\) 13.2639 0.868949 0.434474 0.900684i \(-0.356934\pi\)
0.434474 + 0.900684i \(0.356934\pi\)
\(234\) 38.6533 2.52685
\(235\) −22.6785 −1.47938
\(236\) −30.3344 −1.97460
\(237\) −37.8465 −2.45839
\(238\) 55.1449 3.57451
\(239\) 1.16799 0.0755509 0.0377755 0.999286i \(-0.487973\pi\)
0.0377755 + 0.999286i \(0.487973\pi\)
\(240\) −152.831 −9.86521
\(241\) 17.7842 1.14558 0.572790 0.819702i \(-0.305861\pi\)
0.572790 + 0.819702i \(0.305861\pi\)
\(242\) 25.9383 1.66738
\(243\) 20.3165 1.30330
\(244\) −79.8816 −5.11390
\(245\) 49.8671 3.18589
\(246\) −55.9698 −3.56850
\(247\) −14.6199 −0.930240
\(248\) 25.8767 1.64317
\(249\) −6.78687 −0.430100
\(250\) 8.62205 0.545307
\(251\) −15.0140 −0.947672 −0.473836 0.880613i \(-0.657131\pi\)
−0.473836 + 0.880613i \(0.657131\pi\)
\(252\) 120.336 7.58044
\(253\) 1.80229 0.113309
\(254\) 43.5111 2.73013
\(255\) 32.4212 2.03029
\(256\) 121.261 7.57884
\(257\) −2.14831 −0.134008 −0.0670039 0.997753i \(-0.521344\pi\)
−0.0670039 + 0.997753i \(0.521344\pi\)
\(258\) −35.2587 −2.19511
\(259\) −4.86255 −0.302144
\(260\) −57.9697 −3.59513
\(261\) 24.8738 1.53965
\(262\) 58.4125 3.60874
\(263\) −0.0603126 −0.00371903 −0.00185952 0.999998i \(-0.500592\pi\)
−0.00185952 + 0.999998i \(0.500592\pi\)
\(264\) −39.1496 −2.40949
\(265\) 7.96102 0.489042
\(266\) −60.9410 −3.73653
\(267\) −3.35494 −0.205319
\(268\) −85.4590 −5.22024
\(269\) 25.9608 1.58286 0.791430 0.611260i \(-0.209337\pi\)
0.791430 + 0.611260i \(0.209337\pi\)
\(270\) 26.9656 1.64107
\(271\) −2.16211 −0.131339 −0.0656694 0.997841i \(-0.520918\pi\)
−0.0656694 + 0.997841i \(0.520918\pi\)
\(272\) −76.7341 −4.65269
\(273\) 42.7643 2.58821
\(274\) −38.0717 −2.30000
\(275\) −5.29307 −0.319184
\(276\) 21.4279 1.28981
\(277\) 2.49388 0.149842 0.0749212 0.997189i \(-0.476129\pi\)
0.0749212 + 0.997189i \(0.476129\pi\)
\(278\) 27.6240 1.65678
\(279\) −9.89728 −0.592535
\(280\) −159.740 −9.54631
\(281\) 24.6016 1.46761 0.733805 0.679360i \(-0.237743\pi\)
0.733805 + 0.679360i \(0.237743\pi\)
\(282\) −57.0673 −3.39831
\(283\) −30.5285 −1.81473 −0.907367 0.420339i \(-0.861911\pi\)
−0.907367 + 0.420339i \(0.861911\pi\)
\(284\) −65.1116 −3.86367
\(285\) −35.8288 −2.12232
\(286\) −12.2692 −0.725496
\(287\) −36.0993 −2.13088
\(288\) −132.230 −7.79174
\(289\) −0.721838 −0.0424611
\(290\) −49.9477 −2.93303
\(291\) 30.4790 1.78671
\(292\) 41.5570 2.43194
\(293\) 5.32044 0.310824 0.155412 0.987850i \(-0.450330\pi\)
0.155412 + 0.987850i \(0.450330\pi\)
\(294\) 125.484 7.31836
\(295\) −15.4015 −0.896709
\(296\) 10.9649 0.637322
\(297\) 4.26254 0.247338
\(298\) −46.9801 −2.72148
\(299\) 4.43933 0.256733
\(300\) −62.9310 −3.63332
\(301\) −22.7411 −1.31077
\(302\) 22.7237 1.30760
\(303\) 8.68335 0.498845
\(304\) 84.7994 4.86358
\(305\) −40.5577 −2.32233
\(306\) 47.5612 2.71889
\(307\) 10.6136 0.605753 0.302876 0.953030i \(-0.402053\pi\)
0.302876 + 0.953030i \(0.402053\pi\)
\(308\) −38.1967 −2.17646
\(309\) −18.5768 −1.05680
\(310\) 19.8741 1.12878
\(311\) 21.3873 1.21276 0.606381 0.795174i \(-0.292621\pi\)
0.606381 + 0.795174i \(0.292621\pi\)
\(312\) −96.4321 −5.45939
\(313\) −18.5621 −1.04919 −0.524597 0.851351i \(-0.675784\pi\)
−0.524597 + 0.851351i \(0.675784\pi\)
\(314\) −14.5161 −0.819189
\(315\) 61.0972 3.44244
\(316\) 83.2654 4.68404
\(317\) 1.20282 0.0675573 0.0337787 0.999429i \(-0.489246\pi\)
0.0337787 + 0.999429i \(0.489246\pi\)
\(318\) 20.0328 1.12339
\(319\) −7.89539 −0.442057
\(320\) 151.561 8.47254
\(321\) −6.09513 −0.340197
\(322\) 18.5048 1.03123
\(323\) −17.9891 −1.00094
\(324\) −23.5637 −1.30909
\(325\) −13.0377 −0.723203
\(326\) −25.8509 −1.43175
\(327\) 2.68213 0.148322
\(328\) 81.4028 4.49472
\(329\) −36.8072 −2.02925
\(330\) −30.0682 −1.65520
\(331\) −11.0526 −0.607508 −0.303754 0.952750i \(-0.598240\pi\)
−0.303754 + 0.952750i \(0.598240\pi\)
\(332\) 14.9317 0.819482
\(333\) −4.19384 −0.229821
\(334\) −2.26510 −0.123941
\(335\) −43.3895 −2.37062
\(336\) −248.045 −13.5320
\(337\) 6.27586 0.341868 0.170934 0.985282i \(-0.445322\pi\)
0.170934 + 0.985282i \(0.445322\pi\)
\(338\) 6.31993 0.343759
\(339\) 37.6816 2.04658
\(340\) −71.3292 −3.86837
\(341\) 3.14157 0.170126
\(342\) −52.5602 −2.84213
\(343\) 46.8964 2.53217
\(344\) 51.2804 2.76486
\(345\) 10.8795 0.585730
\(346\) 58.0295 3.11969
\(347\) 9.86961 0.529828 0.264914 0.964272i \(-0.414656\pi\)
0.264914 + 0.964272i \(0.414656\pi\)
\(348\) −93.8708 −5.03200
\(349\) −7.92123 −0.424014 −0.212007 0.977268i \(-0.568000\pi\)
−0.212007 + 0.977268i \(0.568000\pi\)
\(350\) −54.3461 −2.90492
\(351\) 10.4994 0.560414
\(352\) 41.9722 2.23713
\(353\) 16.5909 0.883043 0.441521 0.897251i \(-0.354439\pi\)
0.441521 + 0.897251i \(0.354439\pi\)
\(354\) −38.7557 −2.05984
\(355\) −33.0587 −1.75457
\(356\) 7.38114 0.391199
\(357\) 52.6196 2.78492
\(358\) −17.4586 −0.922717
\(359\) 25.4669 1.34409 0.672045 0.740510i \(-0.265416\pi\)
0.672045 + 0.740510i \(0.265416\pi\)
\(360\) −137.772 −7.26124
\(361\) 0.879864 0.0463086
\(362\) 8.91590 0.468609
\(363\) 24.7505 1.29906
\(364\) −94.0849 −4.93139
\(365\) 21.0995 1.10440
\(366\) −102.058 −5.33465
\(367\) 26.7846 1.39814 0.699072 0.715051i \(-0.253597\pi\)
0.699072 + 0.715051i \(0.253597\pi\)
\(368\) −25.7494 −1.34228
\(369\) −31.1348 −1.62081
\(370\) 8.42140 0.437808
\(371\) 12.9207 0.670812
\(372\) 37.3511 1.93656
\(373\) −6.31516 −0.326986 −0.163493 0.986544i \(-0.552276\pi\)
−0.163493 + 0.986544i \(0.552276\pi\)
\(374\) −15.0968 −0.780635
\(375\) 8.22721 0.424851
\(376\) 82.9991 4.28035
\(377\) −19.4477 −1.00161
\(378\) 43.7652 2.25104
\(379\) 0.633469 0.0325391 0.0162696 0.999868i \(-0.494821\pi\)
0.0162696 + 0.999868i \(0.494821\pi\)
\(380\) 78.8263 4.04371
\(381\) 41.5185 2.12706
\(382\) 71.1159 3.63861
\(383\) −30.6755 −1.56744 −0.783722 0.621112i \(-0.786681\pi\)
−0.783722 + 0.621112i \(0.786681\pi\)
\(384\) 212.250 10.8313
\(385\) −19.3933 −0.988376
\(386\) 24.1789 1.23067
\(387\) −19.6137 −0.997019
\(388\) −67.0564 −3.40427
\(389\) −20.4414 −1.03642 −0.518211 0.855253i \(-0.673402\pi\)
−0.518211 + 0.855253i \(0.673402\pi\)
\(390\) −74.0630 −3.75032
\(391\) 5.46240 0.276246
\(392\) −182.504 −9.21786
\(393\) 55.7376 2.81159
\(394\) −13.7667 −0.693556
\(395\) 42.2757 2.12712
\(396\) −32.9438 −1.65549
\(397\) 13.3793 0.671489 0.335745 0.941953i \(-0.391012\pi\)
0.335745 + 0.941953i \(0.391012\pi\)
\(398\) 6.22636 0.312099
\(399\) −58.1502 −2.91115
\(400\) 75.6225 3.78113
\(401\) 20.8625 1.04182 0.520912 0.853610i \(-0.325592\pi\)
0.520912 + 0.853610i \(0.325592\pi\)
\(402\) −109.184 −5.44559
\(403\) 7.73821 0.385468
\(404\) −19.1041 −0.950463
\(405\) −11.9638 −0.594487
\(406\) −81.0651 −4.02319
\(407\) 1.33120 0.0659850
\(408\) −118.655 −5.87432
\(409\) 18.9188 0.935473 0.467736 0.883868i \(-0.345070\pi\)
0.467736 + 0.883868i \(0.345070\pi\)
\(410\) 62.5200 3.08764
\(411\) −36.3282 −1.79194
\(412\) 40.8704 2.01354
\(413\) −24.9966 −1.23000
\(414\) 15.9599 0.784389
\(415\) 7.58115 0.372144
\(416\) 103.385 5.06885
\(417\) 26.3590 1.29081
\(418\) 16.6835 0.816018
\(419\) 6.28932 0.307253 0.153627 0.988129i \(-0.450905\pi\)
0.153627 + 0.988129i \(0.450905\pi\)
\(420\) −230.573 −11.2508
\(421\) −3.87669 −0.188938 −0.0944691 0.995528i \(-0.530115\pi\)
−0.0944691 + 0.995528i \(0.530115\pi\)
\(422\) −49.8480 −2.42656
\(423\) −31.7454 −1.54351
\(424\) −29.1359 −1.41496
\(425\) −16.0423 −0.778168
\(426\) −83.1876 −4.03045
\(427\) −65.8252 −3.18550
\(428\) 13.4098 0.648186
\(429\) −11.7074 −0.565238
\(430\) 39.3850 1.89932
\(431\) −34.9383 −1.68292 −0.841459 0.540320i \(-0.818303\pi\)
−0.841459 + 0.540320i \(0.818303\pi\)
\(432\) −60.8992 −2.93002
\(433\) −5.20144 −0.249965 −0.124983 0.992159i \(-0.539888\pi\)
−0.124983 + 0.992159i \(0.539888\pi\)
\(434\) 32.2557 1.54832
\(435\) −47.6603 −2.28514
\(436\) −5.90091 −0.282602
\(437\) −6.03654 −0.288767
\(438\) 53.0939 2.53692
\(439\) 21.3471 1.01884 0.509421 0.860518i \(-0.329860\pi\)
0.509421 + 0.860518i \(0.329860\pi\)
\(440\) 43.7313 2.08481
\(441\) 69.8040 3.32400
\(442\) −37.1859 −1.76875
\(443\) 38.9121 1.84877 0.924386 0.381459i \(-0.124578\pi\)
0.924386 + 0.381459i \(0.124578\pi\)
\(444\) 15.8270 0.751117
\(445\) 3.74757 0.177652
\(446\) 48.9863 2.31957
\(447\) −44.8286 −2.12032
\(448\) 245.984 11.6217
\(449\) −2.39938 −0.113234 −0.0566170 0.998396i \(-0.518031\pi\)
−0.0566170 + 0.998396i \(0.518031\pi\)
\(450\) −46.8722 −2.20958
\(451\) 9.88274 0.465360
\(452\) −82.9025 −3.89940
\(453\) 21.6831 1.01876
\(454\) 11.9796 0.562231
\(455\) −47.7690 −2.23945
\(456\) 131.127 6.14058
\(457\) 26.3377 1.23203 0.616014 0.787735i \(-0.288746\pi\)
0.616014 + 0.787735i \(0.288746\pi\)
\(458\) −52.0678 −2.43297
\(459\) 12.9190 0.603007
\(460\) −23.9357 −1.11601
\(461\) −6.62506 −0.308560 −0.154280 0.988027i \(-0.549306\pi\)
−0.154280 + 0.988027i \(0.549306\pi\)
\(462\) −48.8007 −2.27041
\(463\) −5.93727 −0.275929 −0.137964 0.990437i \(-0.544056\pi\)
−0.137964 + 0.990437i \(0.544056\pi\)
\(464\) 112.802 5.23670
\(465\) 18.9640 0.879435
\(466\) −37.2830 −1.72710
\(467\) −22.5706 −1.04444 −0.522222 0.852810i \(-0.674897\pi\)
−0.522222 + 0.852810i \(0.674897\pi\)
\(468\) −81.1460 −3.75098
\(469\) −70.4211 −3.25175
\(470\) 63.7460 2.94038
\(471\) −13.8513 −0.638235
\(472\) 56.3665 2.59448
\(473\) 6.22572 0.286259
\(474\) 106.381 4.88624
\(475\) 17.7285 0.813439
\(476\) −115.767 −5.30619
\(477\) 11.1438 0.510242
\(478\) −3.28305 −0.150163
\(479\) −41.1560 −1.88047 −0.940234 0.340530i \(-0.889394\pi\)
−0.940234 + 0.340530i \(0.889394\pi\)
\(480\) 253.364 11.5644
\(481\) 3.27896 0.149508
\(482\) −49.9888 −2.27693
\(483\) 17.6574 0.803438
\(484\) −54.4531 −2.47514
\(485\) −34.0460 −1.54595
\(486\) −57.1067 −2.59041
\(487\) −6.66629 −0.302078 −0.151039 0.988528i \(-0.548262\pi\)
−0.151039 + 0.988528i \(0.548262\pi\)
\(488\) 148.434 6.71927
\(489\) −24.6671 −1.11548
\(490\) −140.169 −6.33220
\(491\) −7.31656 −0.330192 −0.165096 0.986278i \(-0.552793\pi\)
−0.165096 + 0.986278i \(0.552793\pi\)
\(492\) 117.499 5.29726
\(493\) −23.9295 −1.07773
\(494\) 41.0943 1.84892
\(495\) −16.7263 −0.751792
\(496\) −44.8838 −2.01534
\(497\) −53.6542 −2.40672
\(498\) 19.0769 0.854857
\(499\) −18.1881 −0.814209 −0.407105 0.913382i \(-0.633462\pi\)
−0.407105 + 0.913382i \(0.633462\pi\)
\(500\) −18.1005 −0.809480
\(501\) −2.16137 −0.0965630
\(502\) 42.2021 1.88357
\(503\) −42.3410 −1.88789 −0.943945 0.330102i \(-0.892917\pi\)
−0.943945 + 0.330102i \(0.892917\pi\)
\(504\) −223.604 −9.96013
\(505\) −9.69957 −0.431625
\(506\) −5.06597 −0.225210
\(507\) 6.03051 0.267824
\(508\) −91.3442 −4.05274
\(509\) 23.9738 1.06262 0.531310 0.847178i \(-0.321700\pi\)
0.531310 + 0.847178i \(0.321700\pi\)
\(510\) −91.1312 −4.03536
\(511\) 34.2444 1.51488
\(512\) −182.579 −8.06892
\(513\) −14.2769 −0.630339
\(514\) 6.03859 0.266351
\(515\) 20.7508 0.914392
\(516\) 74.0196 3.25853
\(517\) 10.0765 0.443166
\(518\) 13.6679 0.600534
\(519\) 55.3721 2.43056
\(520\) 107.718 4.72373
\(521\) −9.43141 −0.413198 −0.206599 0.978426i \(-0.566239\pi\)
−0.206599 + 0.978426i \(0.566239\pi\)
\(522\) −69.9168 −3.06017
\(523\) 17.6670 0.772523 0.386262 0.922389i \(-0.373766\pi\)
0.386262 + 0.922389i \(0.373766\pi\)
\(524\) −122.627 −5.35699
\(525\) −51.8573 −2.26324
\(526\) 0.169530 0.00739186
\(527\) 9.52153 0.414764
\(528\) 67.9061 2.95523
\(529\) −21.1670 −0.920304
\(530\) −22.3773 −0.972007
\(531\) −21.5590 −0.935581
\(532\) 127.935 5.54669
\(533\) 24.3428 1.05441
\(534\) 9.43025 0.408087
\(535\) 6.80845 0.294355
\(536\) 158.797 6.85900
\(537\) −16.6591 −0.718894
\(538\) −72.9722 −3.14605
\(539\) −22.1570 −0.954370
\(540\) −56.6097 −2.43609
\(541\) 12.4410 0.534881 0.267441 0.963574i \(-0.413822\pi\)
0.267441 + 0.963574i \(0.413822\pi\)
\(542\) 6.07738 0.261046
\(543\) 8.50760 0.365096
\(544\) 127.210 5.45409
\(545\) −2.99603 −0.128336
\(546\) −120.204 −5.14427
\(547\) 16.9857 0.726257 0.363128 0.931739i \(-0.381709\pi\)
0.363128 + 0.931739i \(0.381709\pi\)
\(548\) 79.9250 3.41423
\(549\) −56.7727 −2.42300
\(550\) 14.8781 0.634403
\(551\) 26.4446 1.12658
\(552\) −39.8168 −1.69471
\(553\) 68.6135 2.91774
\(554\) −7.00992 −0.297823
\(555\) 8.03574 0.341098
\(556\) −57.9919 −2.45941
\(557\) −12.2201 −0.517783 −0.258892 0.965906i \(-0.583357\pi\)
−0.258892 + 0.965906i \(0.583357\pi\)
\(558\) 27.8198 1.17771
\(559\) 15.3350 0.648601
\(560\) 277.074 11.7085
\(561\) −14.4054 −0.608197
\(562\) −69.1516 −2.91698
\(563\) −24.1750 −1.01885 −0.509426 0.860514i \(-0.670142\pi\)
−0.509426 + 0.860514i \(0.670142\pi\)
\(564\) 119.803 5.04462
\(565\) −42.0915 −1.77080
\(566\) 85.8113 3.60692
\(567\) −19.4173 −0.815450
\(568\) 120.989 5.07657
\(569\) 19.2414 0.806642 0.403321 0.915058i \(-0.367856\pi\)
0.403321 + 0.915058i \(0.367856\pi\)
\(570\) 100.710 4.21826
\(571\) 31.6459 1.32434 0.662169 0.749354i \(-0.269636\pi\)
0.662169 + 0.749354i \(0.269636\pi\)
\(572\) 25.7572 1.07696
\(573\) 67.8592 2.83486
\(574\) 101.470 4.23528
\(575\) −5.38327 −0.224498
\(576\) 212.156 8.83982
\(577\) 17.4190 0.725164 0.362582 0.931952i \(-0.381895\pi\)
0.362582 + 0.931952i \(0.381895\pi\)
\(578\) 2.02898 0.0843946
\(579\) 23.0716 0.958823
\(580\) 104.857 4.35393
\(581\) 12.3042 0.510464
\(582\) −85.6722 −3.55123
\(583\) −3.53725 −0.146498
\(584\) −77.2201 −3.19539
\(585\) −41.1997 −1.70340
\(586\) −14.9550 −0.617785
\(587\) −4.81384 −0.198688 −0.0993442 0.995053i \(-0.531674\pi\)
−0.0993442 + 0.995053i \(0.531674\pi\)
\(588\) −263.432 −10.8637
\(589\) −10.5223 −0.433564
\(590\) 43.2913 1.78228
\(591\) −13.1363 −0.540353
\(592\) −19.0189 −0.781673
\(593\) 33.3451 1.36932 0.684660 0.728862i \(-0.259951\pi\)
0.684660 + 0.728862i \(0.259951\pi\)
\(594\) −11.9814 −0.491603
\(595\) −58.7777 −2.40965
\(596\) 98.6266 4.03990
\(597\) 5.94123 0.243158
\(598\) −12.4783 −0.510277
\(599\) 9.78236 0.399696 0.199848 0.979827i \(-0.435955\pi\)
0.199848 + 0.979827i \(0.435955\pi\)
\(600\) 116.937 4.77391
\(601\) 46.9041 1.91326 0.956629 0.291310i \(-0.0940911\pi\)
0.956629 + 0.291310i \(0.0940911\pi\)
\(602\) 63.9219 2.60526
\(603\) −60.7366 −2.47339
\(604\) −47.7045 −1.94107
\(605\) −27.6471 −1.12401
\(606\) −24.4076 −0.991493
\(607\) −31.5165 −1.27921 −0.639607 0.768702i \(-0.720903\pi\)
−0.639607 + 0.768702i \(0.720903\pi\)
\(608\) −140.581 −5.70130
\(609\) −77.3527 −3.13449
\(610\) 114.002 4.61580
\(611\) 24.8202 1.00412
\(612\) −99.8466 −4.03606
\(613\) 3.67915 0.148600 0.0742998 0.997236i \(-0.476328\pi\)
0.0742998 + 0.997236i \(0.476328\pi\)
\(614\) −29.8334 −1.20398
\(615\) 59.6569 2.40560
\(616\) 70.9760 2.85970
\(617\) −6.17204 −0.248477 −0.124239 0.992252i \(-0.539649\pi\)
−0.124239 + 0.992252i \(0.539649\pi\)
\(618\) 52.2167 2.10046
\(619\) −12.9977 −0.522420 −0.261210 0.965282i \(-0.584121\pi\)
−0.261210 + 0.965282i \(0.584121\pi\)
\(620\) −41.7223 −1.67561
\(621\) 4.33518 0.173965
\(622\) −60.1166 −2.41046
\(623\) 6.08231 0.243683
\(624\) 167.264 6.69592
\(625\) −29.0709 −1.16284
\(626\) 52.1755 2.08535
\(627\) 15.9195 0.635764
\(628\) 30.4740 1.21605
\(629\) 4.03462 0.160871
\(630\) −171.736 −6.84211
\(631\) −38.7519 −1.54269 −0.771344 0.636418i \(-0.780415\pi\)
−0.771344 + 0.636418i \(0.780415\pi\)
\(632\) −154.721 −6.15448
\(633\) −47.5652 −1.89055
\(634\) −3.38097 −0.134275
\(635\) −46.3775 −1.84044
\(636\) −42.0555 −1.66761
\(637\) −54.5764 −2.16240
\(638\) 22.1928 0.878622
\(639\) −46.2755 −1.83063
\(640\) −237.090 −9.37180
\(641\) −7.05938 −0.278829 −0.139414 0.990234i \(-0.544522\pi\)
−0.139414 + 0.990234i \(0.544522\pi\)
\(642\) 17.1325 0.676167
\(643\) −15.2687 −0.602140 −0.301070 0.953602i \(-0.597344\pi\)
−0.301070 + 0.953602i \(0.597344\pi\)
\(644\) −38.8476 −1.53081
\(645\) 37.5814 1.47977
\(646\) 50.5648 1.98944
\(647\) −28.4191 −1.11727 −0.558635 0.829414i \(-0.688675\pi\)
−0.558635 + 0.829414i \(0.688675\pi\)
\(648\) 43.7854 1.72005
\(649\) 6.84320 0.268619
\(650\) 36.6472 1.43742
\(651\) 30.7786 1.20631
\(652\) 54.2696 2.12536
\(653\) 41.4163 1.62074 0.810372 0.585916i \(-0.199265\pi\)
0.810372 + 0.585916i \(0.199265\pi\)
\(654\) −7.53909 −0.294802
\(655\) −62.2606 −2.43272
\(656\) −141.195 −5.51276
\(657\) 29.5350 1.15227
\(658\) 103.460 4.03328
\(659\) 14.2736 0.556020 0.278010 0.960578i \(-0.410325\pi\)
0.278010 + 0.960578i \(0.410325\pi\)
\(660\) 63.1230 2.45706
\(661\) −15.6146 −0.607337 −0.303668 0.952778i \(-0.598212\pi\)
−0.303668 + 0.952778i \(0.598212\pi\)
\(662\) 31.0674 1.20747
\(663\) −35.4829 −1.37804
\(664\) −27.7456 −1.07674
\(665\) 64.9556 2.51887
\(666\) 11.7883 0.456786
\(667\) −8.02994 −0.310920
\(668\) 4.75520 0.183984
\(669\) 46.7429 1.80719
\(670\) 121.962 4.71179
\(671\) 18.0207 0.695680
\(672\) 411.210 15.8628
\(673\) −20.4865 −0.789696 −0.394848 0.918747i \(-0.629203\pi\)
−0.394848 + 0.918747i \(0.629203\pi\)
\(674\) −17.6405 −0.679488
\(675\) −12.7318 −0.490049
\(676\) −13.2676 −0.510292
\(677\) 45.4249 1.74582 0.872911 0.487880i \(-0.162230\pi\)
0.872911 + 0.487880i \(0.162230\pi\)
\(678\) −105.917 −4.06773
\(679\) −55.2567 −2.12056
\(680\) 132.542 5.08275
\(681\) 11.4310 0.438037
\(682\) −8.83050 −0.338137
\(683\) 27.3934 1.04818 0.524090 0.851663i \(-0.324406\pi\)
0.524090 + 0.851663i \(0.324406\pi\)
\(684\) 110.341 4.21900
\(685\) 40.5797 1.55047
\(686\) −131.819 −5.03288
\(687\) −49.6834 −1.89554
\(688\) −88.9473 −3.39109
\(689\) −8.71284 −0.331933
\(690\) −30.5806 −1.16418
\(691\) −7.67251 −0.291876 −0.145938 0.989294i \(-0.546620\pi\)
−0.145938 + 0.989294i \(0.546620\pi\)
\(692\) −121.823 −4.63102
\(693\) −27.1468 −1.03122
\(694\) −27.7421 −1.05307
\(695\) −29.4438 −1.11687
\(696\) 174.428 6.61167
\(697\) 29.9528 1.13454
\(698\) 22.2654 0.842759
\(699\) −35.5756 −1.34559
\(700\) 114.090 4.31221
\(701\) 5.82316 0.219938 0.109969 0.993935i \(-0.464925\pi\)
0.109969 + 0.993935i \(0.464925\pi\)
\(702\) −29.5122 −1.11387
\(703\) −4.45868 −0.168162
\(704\) −67.3419 −2.53804
\(705\) 60.8268 2.29087
\(706\) −46.6345 −1.75511
\(707\) −15.7424 −0.592054
\(708\) 81.3610 3.05773
\(709\) −49.6360 −1.86412 −0.932059 0.362306i \(-0.881990\pi\)
−0.932059 + 0.362306i \(0.881990\pi\)
\(710\) 92.9231 3.48734
\(711\) 59.1776 2.21933
\(712\) −13.7154 −0.514007
\(713\) 3.19511 0.119658
\(714\) −147.906 −5.53524
\(715\) 13.0775 0.489071
\(716\) 36.6514 1.36973
\(717\) −3.13270 −0.116993
\(718\) −71.5837 −2.67148
\(719\) 31.9469 1.19142 0.595710 0.803200i \(-0.296871\pi\)
0.595710 + 0.803200i \(0.296871\pi\)
\(720\) 238.970 8.90588
\(721\) 33.6786 1.25426
\(722\) −2.47317 −0.0920419
\(723\) −47.6995 −1.77396
\(724\) −18.7174 −0.695627
\(725\) 23.5829 0.875845
\(726\) −69.5700 −2.58199
\(727\) −26.9356 −0.998985 −0.499492 0.866318i \(-0.666480\pi\)
−0.499492 + 0.866318i \(0.666480\pi\)
\(728\) 174.826 6.47947
\(729\) −42.5118 −1.57451
\(730\) −59.3075 −2.19507
\(731\) 18.8690 0.697897
\(732\) 214.253 7.91902
\(733\) −46.9660 −1.73473 −0.867364 0.497674i \(-0.834188\pi\)
−0.867364 + 0.497674i \(0.834188\pi\)
\(734\) −75.2876 −2.77892
\(735\) −133.750 −4.93345
\(736\) 42.6875 1.57348
\(737\) 19.2789 0.710146
\(738\) 87.5155 3.22149
\(739\) 38.7073 1.42387 0.711935 0.702245i \(-0.247819\pi\)
0.711935 + 0.702245i \(0.247819\pi\)
\(740\) −17.6793 −0.649903
\(741\) 39.2124 1.44050
\(742\) −36.3184 −1.33329
\(743\) −33.0476 −1.21240 −0.606200 0.795312i \(-0.707307\pi\)
−0.606200 + 0.795312i \(0.707307\pi\)
\(744\) −69.4047 −2.54450
\(745\) 50.0750 1.83461
\(746\) 17.7510 0.649910
\(747\) 10.6121 0.388276
\(748\) 31.6931 1.15881
\(749\) 11.0501 0.403762
\(750\) −23.1255 −0.844424
\(751\) −20.4705 −0.746978 −0.373489 0.927635i \(-0.621839\pi\)
−0.373489 + 0.927635i \(0.621839\pi\)
\(752\) −143.964 −5.24983
\(753\) 40.2694 1.46750
\(754\) 54.6646 1.99077
\(755\) −24.2207 −0.881480
\(756\) −91.8775 −3.34155
\(757\) 49.7058 1.80659 0.903295 0.429021i \(-0.141141\pi\)
0.903295 + 0.429021i \(0.141141\pi\)
\(758\) −1.78059 −0.0646739
\(759\) −4.83397 −0.175462
\(760\) −146.473 −5.31312
\(761\) −44.6502 −1.61857 −0.809284 0.587418i \(-0.800145\pi\)
−0.809284 + 0.587418i \(0.800145\pi\)
\(762\) −116.703 −4.22769
\(763\) −4.86255 −0.176036
\(764\) −149.296 −5.40133
\(765\) −50.6944 −1.83286
\(766\) 86.2243 3.11541
\(767\) 16.8560 0.608633
\(768\) −325.239 −11.7361
\(769\) 1.02444 0.0369424 0.0184712 0.999829i \(-0.494120\pi\)
0.0184712 + 0.999829i \(0.494120\pi\)
\(770\) 54.5119 1.96447
\(771\) 5.76205 0.207515
\(772\) −50.7594 −1.82687
\(773\) 6.51487 0.234324 0.117162 0.993113i \(-0.462620\pi\)
0.117162 + 0.993113i \(0.462620\pi\)
\(774\) 55.1312 1.98165
\(775\) −9.38360 −0.337069
\(776\) 124.602 4.47296
\(777\) 13.0420 0.467880
\(778\) 57.4579 2.05997
\(779\) −33.1010 −1.18597
\(780\) 155.483 5.56717
\(781\) 14.6887 0.525602
\(782\) −15.3540 −0.549059
\(783\) −18.9914 −0.678697
\(784\) 316.559 11.3057
\(785\) 15.4723 0.552232
\(786\) −156.670 −5.58824
\(787\) 6.86513 0.244716 0.122358 0.992486i \(-0.460954\pi\)
0.122358 + 0.992486i \(0.460954\pi\)
\(788\) 28.9008 1.02955
\(789\) 0.161766 0.00575903
\(790\) −118.831 −4.22782
\(791\) −68.3145 −2.42898
\(792\) 61.2152 2.17519
\(793\) 44.3879 1.57626
\(794\) −37.6074 −1.33464
\(795\) −21.3525 −0.757296
\(796\) −13.0712 −0.463296
\(797\) −43.9442 −1.55658 −0.778291 0.627903i \(-0.783913\pi\)
−0.778291 + 0.627903i \(0.783913\pi\)
\(798\) 163.452 5.78613
\(799\) 30.5402 1.08043
\(800\) −125.367 −4.43240
\(801\) 5.24585 0.185353
\(802\) −58.6415 −2.07070
\(803\) −9.37494 −0.330834
\(804\) 229.212 8.08370
\(805\) −19.7238 −0.695173
\(806\) −21.7510 −0.766146
\(807\) −69.6304 −2.45111
\(808\) 35.4986 1.24884
\(809\) 31.0335 1.09108 0.545540 0.838085i \(-0.316325\pi\)
0.545540 + 0.838085i \(0.316325\pi\)
\(810\) 33.6286 1.18159
\(811\) −31.9230 −1.12097 −0.560484 0.828165i \(-0.689385\pi\)
−0.560484 + 0.828165i \(0.689385\pi\)
\(812\) 170.182 5.97223
\(813\) 5.79907 0.203382
\(814\) −3.74181 −0.131150
\(815\) 27.5539 0.965172
\(816\) 205.811 7.20483
\(817\) −20.8523 −0.729529
\(818\) −53.1779 −1.85932
\(819\) −66.8671 −2.33653
\(820\) −131.250 −4.58345
\(821\) −12.2379 −0.427106 −0.213553 0.976931i \(-0.568504\pi\)
−0.213553 + 0.976931i \(0.568504\pi\)
\(822\) 102.113 3.56161
\(823\) −33.0179 −1.15093 −0.575466 0.817826i \(-0.695179\pi\)
−0.575466 + 0.817826i \(0.695179\pi\)
\(824\) −75.9442 −2.64564
\(825\) 14.1967 0.494267
\(826\) 70.2618 2.44472
\(827\) 27.2516 0.947632 0.473816 0.880624i \(-0.342876\pi\)
0.473816 + 0.880624i \(0.342876\pi\)
\(828\) −33.5052 −1.16439
\(829\) 12.8356 0.445797 0.222899 0.974842i \(-0.428448\pi\)
0.222899 + 0.974842i \(0.428448\pi\)
\(830\) −21.3095 −0.739664
\(831\) −6.68891 −0.232036
\(832\) −165.874 −5.75066
\(833\) −67.1539 −2.32674
\(834\) −74.0914 −2.56557
\(835\) 2.41432 0.0835510
\(836\) −35.0242 −1.21134
\(837\) 7.55666 0.261197
\(838\) −17.6784 −0.610689
\(839\) −23.4493 −0.809559 −0.404779 0.914414i \(-0.632652\pi\)
−0.404779 + 0.914414i \(0.632652\pi\)
\(840\) 428.445 14.7827
\(841\) 6.17726 0.213009
\(842\) 10.8968 0.375529
\(843\) −65.9848 −2.27264
\(844\) 104.647 3.60211
\(845\) −6.73626 −0.231734
\(846\) 89.2317 3.06785
\(847\) −44.8712 −1.54179
\(848\) 50.5370 1.73545
\(849\) 81.8816 2.81017
\(850\) 45.0927 1.54667
\(851\) 1.35388 0.0464105
\(852\) 174.638 5.98300
\(853\) 38.2265 1.30885 0.654425 0.756127i \(-0.272911\pi\)
0.654425 + 0.756127i \(0.272911\pi\)
\(854\) 185.025 6.33143
\(855\) 56.0227 1.91594
\(856\) −24.9176 −0.851667
\(857\) −5.05588 −0.172705 −0.0863527 0.996265i \(-0.527521\pi\)
−0.0863527 + 0.996265i \(0.527521\pi\)
\(858\) 32.9078 1.12345
\(859\) 29.9075 1.02043 0.510216 0.860046i \(-0.329565\pi\)
0.510216 + 0.860046i \(0.329565\pi\)
\(860\) −82.6821 −2.81944
\(861\) 96.8232 3.29973
\(862\) 98.2065 3.34493
\(863\) −48.1847 −1.64023 −0.820113 0.572202i \(-0.806089\pi\)
−0.820113 + 0.572202i \(0.806089\pi\)
\(864\) 100.959 3.43470
\(865\) −61.8523 −2.10304
\(866\) 14.6205 0.496825
\(867\) 1.93607 0.0657523
\(868\) −67.7154 −2.29841
\(869\) −18.7840 −0.637204
\(870\) 133.966 4.54188
\(871\) 47.4871 1.60904
\(872\) 10.9649 0.371318
\(873\) −47.6577 −1.61297
\(874\) 16.9678 0.573946
\(875\) −14.9155 −0.504234
\(876\) −111.462 −3.76594
\(877\) 7.89519 0.266602 0.133301 0.991076i \(-0.457442\pi\)
0.133301 + 0.991076i \(0.457442\pi\)
\(878\) −60.0036 −2.02502
\(879\) −14.2701 −0.481320
\(880\) −75.8533 −2.55701
\(881\) −5.03885 −0.169763 −0.0848816 0.996391i \(-0.527051\pi\)
−0.0848816 + 0.996391i \(0.527051\pi\)
\(882\) −196.209 −6.60670
\(883\) 2.45026 0.0824578 0.0412289 0.999150i \(-0.486873\pi\)
0.0412289 + 0.999150i \(0.486873\pi\)
\(884\) 78.0653 2.62562
\(885\) 41.3088 1.38858
\(886\) −109.376 −3.67457
\(887\) 43.1676 1.44943 0.724713 0.689050i \(-0.241972\pi\)
0.724713 + 0.689050i \(0.241972\pi\)
\(888\) −29.4093 −0.986912
\(889\) −75.2707 −2.52450
\(890\) −10.5339 −0.353096
\(891\) 5.31578 0.178085
\(892\) −102.838 −3.44328
\(893\) −33.7501 −1.12940
\(894\) 126.007 4.21430
\(895\) 18.6088 0.622022
\(896\) −384.797 −12.8552
\(897\) −11.9069 −0.397559
\(898\) 6.74432 0.225061
\(899\) −13.9970 −0.466826
\(900\) 98.4002 3.28001
\(901\) −10.7208 −0.357161
\(902\) −27.7790 −0.924939
\(903\) 60.9946 2.02977
\(904\) 154.047 5.12352
\(905\) −9.50325 −0.315899
\(906\) −60.9480 −2.02486
\(907\) −21.3727 −0.709670 −0.354835 0.934929i \(-0.615463\pi\)
−0.354835 + 0.934929i \(0.615463\pi\)
\(908\) −25.1491 −0.834603
\(909\) −13.5775 −0.450336
\(910\) 134.272 4.45107
\(911\) 3.86748 0.128135 0.0640677 0.997946i \(-0.479593\pi\)
0.0640677 + 0.997946i \(0.479593\pi\)
\(912\) −227.443 −7.53140
\(913\) −3.36846 −0.111480
\(914\) −74.0316 −2.44875
\(915\) 108.781 3.59619
\(916\) 109.308 3.61162
\(917\) −101.049 −3.33693
\(918\) −36.3134 −1.19852
\(919\) 35.3232 1.16521 0.582603 0.812757i \(-0.302034\pi\)
0.582603 + 0.812757i \(0.302034\pi\)
\(920\) 44.4766 1.46635
\(921\) −28.4672 −0.938026
\(922\) 18.6221 0.613286
\(923\) 36.1806 1.19090
\(924\) 102.449 3.37031
\(925\) −3.97617 −0.130736
\(926\) 16.6888 0.548429
\(927\) 29.0470 0.954030
\(928\) −187.004 −6.13870
\(929\) −44.3052 −1.45361 −0.726803 0.686846i \(-0.758995\pi\)
−0.726803 + 0.686846i \(0.758995\pi\)
\(930\) −53.3051 −1.74794
\(931\) 74.2122 2.43221
\(932\) 78.2693 2.56379
\(933\) −57.3636 −1.87800
\(934\) 63.4428 2.07591
\(935\) 16.0913 0.526242
\(936\) 150.783 4.92850
\(937\) 5.55481 0.181468 0.0907339 0.995875i \(-0.471079\pi\)
0.0907339 + 0.995875i \(0.471079\pi\)
\(938\) 197.944 6.46309
\(939\) 49.7861 1.62471
\(940\) −133.824 −4.36485
\(941\) 39.7310 1.29520 0.647598 0.761983i \(-0.275774\pi\)
0.647598 + 0.761983i \(0.275774\pi\)
\(942\) 38.9340 1.26854
\(943\) 10.0512 0.327311
\(944\) −97.7693 −3.18212
\(945\) −46.6483 −1.51747
\(946\) −17.4996 −0.568961
\(947\) 2.06859 0.0672203 0.0336101 0.999435i \(-0.489300\pi\)
0.0336101 + 0.999435i \(0.489300\pi\)
\(948\) −223.329 −7.25338
\(949\) −23.0920 −0.749599
\(950\) −49.8323 −1.61677
\(951\) −3.22613 −0.104615
\(952\) 215.115 6.97193
\(953\) −23.7937 −0.770754 −0.385377 0.922759i \(-0.625929\pi\)
−0.385377 + 0.922759i \(0.625929\pi\)
\(954\) −31.3237 −1.01414
\(955\) −75.8008 −2.45286
\(956\) 6.89220 0.222910
\(957\) 21.1765 0.684539
\(958\) 115.684 3.73757
\(959\) 65.8609 2.12676
\(960\) −406.508 −13.1200
\(961\) −25.4306 −0.820342
\(962\) −9.21669 −0.297158
\(963\) 9.53047 0.307115
\(964\) 104.943 3.37998
\(965\) −25.7717 −0.829620
\(966\) −49.6323 −1.59689
\(967\) 22.6454 0.728227 0.364114 0.931354i \(-0.381372\pi\)
0.364114 + 0.931354i \(0.381372\pi\)
\(968\) 101.183 3.25215
\(969\) 48.2492 1.54999
\(970\) 95.6985 3.07269
\(971\) −47.5343 −1.52545 −0.762724 0.646724i \(-0.776139\pi\)
−0.762724 + 0.646724i \(0.776139\pi\)
\(972\) 119.886 3.84534
\(973\) −47.7873 −1.53199
\(974\) 18.7380 0.600404
\(975\) 34.9689 1.11990
\(976\) −257.462 −8.24117
\(977\) 10.9522 0.350392 0.175196 0.984534i \(-0.443944\pi\)
0.175196 + 0.984534i \(0.443944\pi\)
\(978\) 69.3357 2.21711
\(979\) −1.66513 −0.0532176
\(980\) 294.261 9.39983
\(981\) −4.19384 −0.133899
\(982\) 20.5658 0.656281
\(983\) −0.953264 −0.0304044 −0.0152022 0.999884i \(-0.504839\pi\)
−0.0152022 + 0.999884i \(0.504839\pi\)
\(984\) −218.333 −6.96021
\(985\) 14.6736 0.467540
\(986\) 67.2624 2.14207
\(987\) 98.7218 3.14235
\(988\) −86.2705 −2.74463
\(989\) 6.33182 0.201340
\(990\) 47.0152 1.49424
\(991\) −15.6137 −0.495986 −0.247993 0.968762i \(-0.579771\pi\)
−0.247993 + 0.968762i \(0.579771\pi\)
\(992\) 74.4086 2.36248
\(993\) 29.6447 0.940745
\(994\) 150.814 4.78354
\(995\) −6.63654 −0.210392
\(996\) −40.0487 −1.26899
\(997\) 24.6809 0.781653 0.390826 0.920464i \(-0.372189\pi\)
0.390826 + 0.920464i \(0.372189\pi\)
\(998\) 51.1240 1.61830
\(999\) 3.20203 0.101308
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))